The probability that a particular brand of smoke alarm will function properly and sound an alarm in the presence of smoke is 0.8. You have five such alarms in your home and they operate independently. Which of the following distributions would you use to determine the probability that all of them will function properly in case of a fire?
A) binomial distribution
B) Poisson distribution
C) both of the above
D) none of the above

Question

Quizplus · Accepted Answer

The binomial distribution is appropriate for this scenario, where we have five independent trials (five smoke alarms) and each trial has only two possible outcomes (functioning properly or not). The probability of success (proper functioning of the alarm) is constant for each trial, and we want to calculate the probability of a specific number of successes (in this case, all five alarms functioning properly). Therefore, the binomial distribution can be used to determine the probability that all of the alarms will function properly in case of a fire. The Poisson distribution is not appropriate here because it is used for rare events occurring in a fixed or known time or space interval, whereas in this case we have a fixed number of trials (five smoke alarms) and the events are not rare.

The Probability That a Particular Brand of Smoke Alarm Will